1 Summary

This script runs analyses on data from study 2. Specifically, it compares data from two groups of participants who underwent escapable stress (EC) or yoked inescapable stress (YC), respectively. We use the terms “group” and “condition” interchangeably. . Measurements under investigation comprised reaction times (RTs) and ratings under acute stress (stressor aversiveness, control, exhaustion, helplessness) as well as pre-post changes in affective state (STADI and PANAS questionnaires), and effects escape behaviour (activity, exploration, escapes, efficiency).

2 Sample Descriptives

In total, the sample consisted of N = 100 participants with n = 62 in EC and n = 38 in YC.

2.1 Age & Sex

3 A priori Group Difference Checks

3.1 Sex (Chi-square Test)

## 
##  Pearson's Chi-squared test with Yates' continuity correction
## 
## data:  demo$condition and demo$sex
## X-squared = 0.061738, df = 1, p-value = 0.8038

There were no a priori group differences in male-female ratio.

3.2 Age (t-test)

## 
##  Two Sample t-test
## 
## data:  demo$age[demo$condition == "EC"] and demo$age[demo$condition == "YC"]
## t = -1.758, df = 98, p-value = 0.08186
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  -3.169705  0.191776
## sample estimates:
## mean of x mean of y 
##  22.77419  24.26316
## 
## Cohen's d
## 
## d estimate: -0.362193 (small)
## 95 percent confidence interval:
##       lower       upper 
## -0.77418265  0.04979672

There were some outliers and we checked for the 2 extreme cases but rerunning all analyses without those did not change the results, so we kept them. Overall, there were no differences in age across groups.

3.3 Level of Education

## # A tibble: 1 x 8
##   .y.             group1 group2    n1    n2 statistic     p p.signif
##   <chr>           <chr>  <chr>  <int> <int>     <dbl> <dbl> <chr>   
## 1 education_level EC     YC        62    38     1102. 0.507 ns
## # A tibble: 1 x 7
##   .y.             group1 group2 effsize    n1    n2 magnitude
## * <chr>           <chr>  <chr>    <dbl> <int> <int> <ord>    
## 1 education_level EC     YC      0.0669    62    38 small

There were no a priori group differences with respect to level of education.

4 Manipulation Check

4.1 Verify Yoking of Stress Durations

## 
##  Two Sample t-test
## 
## data:  stress$stress_duration[stress$condition == "EC"] and stress$stress_duration[stress$condition == "YC"]
## t = -0.18889, df = 5998, p-value = 0.8502
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  -0.10778855  0.08884256
## sample estimates:
## mean of x mean of y 
##  7.855990  7.865463

There were no overall differences in overall stress durations between EC and YC because YC participants were pseudoyoked to EC. Very slight timing inaccurracies are due to program execution differences. Note that durations across trials differ between groups. We deliberately introduced a discount of max. stress exposure in EC to enhance the feeling of control. In YC, we randomly shuffled stress durations obtained from EC to enhance the feeling of arbitrary stress durations outside the participant’s control.

4.2 Assess Performance in EC

8 EC participants had less than 30% correct trials, however, excluding them did not affect subsequent results, so we kept them.

4.3 Stressor Aversiveness

There were outliers with particularly low aversiveness ratings which we excluded from this analysis.

## 
## Univariate Type III Repeated-Measures ANOVA Assuming Sphericity
## 
##                  Sum Sq num Df Error SS den Df   F value  Pr(>F)    
## (Intercept)     10059.9      1   788.10     92 1174.3548 < 2e-16 ***
## condition           9.0      1   788.10     92    1.0555 0.30693    
## sex                47.3      1   788.10     92    5.5259 0.02087 *  
## trial               1.9      3   107.59    276    1.6168 0.18571    
## condition:trial     0.4      3   107.59    276    0.3154 0.81422    
## sex:trial           0.9      3   107.59    276    0.7977 0.49603    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## 
## Mauchly Tests for Sphericity
## 
##                 Test statistic    p-value
## trial                  0.62968 6.0129e-08
## condition:trial        0.62968 6.0129e-08
## sex:trial              0.62968 6.0129e-08
## 
## 
## Greenhouse-Geisser and Huynh-Feldt Corrections
##  for Departure from Sphericity
## 
##                  GG eps Pr(>F[GG])
## trial           0.75366     0.1976
## condition:trial 0.75366     0.7562
## sex:trial       0.75366     0.4653
## 
##                    HF eps Pr(>F[HF])
## trial           0.7736208  0.1966629
## condition:trial 0.7736208  0.7617353
## sex:trial       0.7736208  0.4681660
## Anova Table (Type 3 tests)
## 
## Response: aversive_rating
##            Effect           df  MSE      F  pes p.value
## 1       condition        1, 92 8.57   1.06  .01     .31
## 2             sex        1, 92 8.57 5.53 *  .06     .02
## 3           trial 2.26, 208.01 0.52   1.62  .02     .20
## 4 condition:trial 2.26, 208.01 0.52   0.32 .003     .76
## 5       sex:trial 2.26, 208.01 0.52   0.80 .009     .47
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '+' 0.1 ' ' 1
## 
## Sphericity correction method: GG

Both EC and YC rated the stressor as very aversive (global M = 5.3585859). Mean aversiveness ratings did not differ between groups. Stressor aversiveness ratings remained constant over time. Men reported lower stressor aversiveness compared to women.

4.4 Perceived Stressor Controllability

There were some outliers with respect to perceived control and we excluded them since this changed results significantly.

## 
## Univariate Type III Repeated-Measures ANOVA Assuming Sphericity
## 
##                  Sum Sq num Df Error SS den Df  F value    Pr(>F)    
## (Intercept)     2360.74      1   909.35     92 238.8376 < 2.2e-16 ***
## condition        198.43      1   909.35     92  20.0754 2.138e-05 ***
## sex               17.82      1   909.35     92   1.8027  0.182694    
## trial             22.87      3   394.70    276   5.3309  0.001386 ** 
## condition:trial   10.01      3   394.70    276   2.3320  0.074445 .  
## sex:trial          2.72      3   394.70    276   0.6338  0.593787    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## 
## Mauchly Tests for Sphericity
## 
##                 Test statistic    p-value
## trial                  0.77114 0.00026196
## condition:trial        0.77114 0.00026196
## sex:trial              0.77114 0.00026196
## 
## 
## Greenhouse-Geisser and Huynh-Feldt Corrections
##  for Departure from Sphericity
## 
##                  GG eps Pr(>F[GG])   
## trial           0.84333   0.002667 **
## condition:trial 0.84333   0.085560 . 
## sex:trial       0.84333   0.567551   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
##                   HF eps  Pr(>F[HF])
## trial           0.869147 0.002393656
## condition:trial 0.869147 0.083622038
## sex:trial       0.869147 0.572176992
## Anova Table (Type 3 tests)
## 
## Response: control_rating
##            Effect           df  MSE         F  pes p.value
## 1       condition        1, 92 9.88 20.08 ***  .18  <.0001
## 2             sex        1, 92 9.88      1.80  .02     .18
## 3           trial 2.53, 232.76 1.70   5.33 **  .05    .003
## 4 condition:trial 2.53, 232.76 1.70    2.33 +  .02     .09
## 5       sex:trial 2.53, 232.76 1.70      0.63 .007     .57
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '+' 0.1 ' ' 1
## 
## Sphericity correction method: GG
##  contrast  estimate    SE  df t.ratio p.value
##  X15 - X30  -0.4496 0.184 276 -2.446  0.0753 
##  X15 - X45  -0.4031 0.184 276 -2.193  0.1166 
##  X15 - X60  -0.7283 0.184 276 -3.962  0.0006 
##  X30 - X45   0.0465 0.184 276  0.253  0.8004 
##  X30 - X60  -0.2787 0.184 276 -1.516  0.2612 
##  X45 - X60  -0.3252 0.184 276 -1.769  0.2338 
## 
## Results are averaged over the levels of: condition, sex 
## P value adjustment: holm method for 6 tests
## Call:
## bwtrim(formula = control_rating ~ condition * factor(trial), 
##     id = ID, data = ratings_ctrl)
## 
##                           value df1     df2 p.value
## condition               16.7247   1 54.3685  0.0001
## factor(trial)            3.5822   3 45.3750  0.0208
## condition:factor(trial)  3.3395   3 45.3750  0.0274

We observed group differences in perceived control in the expected direction: YC reported lower control than EC. Overall perceived control increased over time (not clear why this would be the case in YC). After removal of outliers, there is a trend for an interaction of condition and trial which reflects EC’s learning curve with greater success in terminating the stressor over time.

5 RTs and Ratings During Stress Exposure

5.1 RTs

There were 3 outliers excluding them did not affect the results, so we kept them.

## Call:
## bwtrim(formula = rt ~ condition * trial, id = ID, data = stress)
## 
##                    value df1      df2 p.value
## trial             1.0098  59 397.3603  0.4609
## condition       530.3995   1 970.8709  0.0000
## trial:condition   0.9437  59 397.7186  0.5958
## [1] -0.8483162
## [1] -0.2205065

EC were significantly faster than YC. There was no effect of trial.

5.2 Exhaustion

There were no outliers with respect to exhaustion ratings.

## 
## Univariate Type III Repeated-Measures ANOVA Assuming Sphericity
## 
##                 Sum Sq num Df Error SS den Df  F value    Pr(>F)    
## (Intercept)     8080.9      1  1172.49     97 668.5348 < 2.2e-16 ***
## condition         29.6      1  1172.49     97   2.4524  0.120600    
## sex               89.6      1  1172.49     97   7.4124  0.007681 ** 
## trial             16.8      3   241.78    291   6.7445  0.000206 ***
## condition:trial    1.7      3   241.78    291   0.7011  0.552033    
## sex:trial          3.8      3   241.78    291   1.5198  0.209463    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## 
## Mauchly Tests for Sphericity
## 
##                 Test statistic    p-value
## trial                  0.61822 8.9693e-09
## condition:trial        0.61822 8.9693e-09
## sex:trial              0.61822 8.9693e-09
## 
## 
## Greenhouse-Geisser and Huynh-Feldt Corrections
##  for Departure from Sphericity
## 
##                  GG eps Pr(>F[GG])    
## trial           0.76833  0.0008058 ***
## condition:trial 0.76833  0.5163622    
## sex:trial       0.76833  0.2182247    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
##                    HF eps   Pr(>F[HF])
## trial           0.7881077 0.0007168391
## condition:trial 0.7881077 0.5197865333
## sex:trial       0.7881077 0.2175475777
## Anova Table (Type 3 tests)
## 
## Response: exhausted_rating
##            Effect           df   MSE        F  pes p.value
## 1       condition        1, 97 12.09     2.45  .02     .12
## 2             sex        1, 97 12.09  7.41 **  .07    .008
## 3           trial 2.30, 223.58  1.08 6.74 ***  .07   .0008
## 4 condition:trial 2.30, 223.58  1.08     0.70 .007     .52
## 5       sex:trial 2.30, 223.58  1.08     1.52  .02     .22
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '+' 0.1 ' ' 1
## 
## Sphericity correction method: GG
##  contrast  estimate    SE  df t.ratio p.value
##  X15 - X30   -0.406 0.134 291 -3.036  0.0131 
##  X15 - X45   -0.560 0.134 291 -4.192  0.0002 
##  X15 - X60   -0.189 0.134 291 -1.416  0.3185 
##  X30 - X45   -0.154 0.134 291 -1.156  0.3185 
##  X30 - X60    0.216 0.134 291  1.621  0.3185 
##  X45 - X60    0.371 0.134 291  2.776  0.0234 
## 
## Results are averaged over the levels of: condition, sex 
## P value adjustment: holm method for 6 tests
## Call:
## bwtrim(formula = exhausted_rating ~ condition * factor(trial), 
##     id = ID, data = ratings)
## 
##                          value df1     df2 p.value
## condition               1.9905   1 73.6712  0.1625
## factor(trial)           6.9634   3 59.6649  0.0004
## condition:factor(trial) 0.9593   3 59.6649  0.4180

There were no group differences in terms of exhaustion ratings. Overall reported exhaustion increased, then decreased over time.

5.3 Feelings of Helplessness

There were no outliers with respect to helplessness ratings.

## 
## Univariate Type III Repeated-Measures ANOVA Assuming Sphericity
## 
##                 Sum Sq num Df Error SS den Df  F value    Pr(>F)    
## (Intercept)     7816.7      1  1165.51     97 650.5440 < 2.2e-16 ***
## condition        112.6      1  1165.51     97   9.3723   0.00285 ** 
## sex               21.5      1  1165.51     97   1.7933   0.18365    
## trial             50.3      3   531.57    291   9.1875 7.944e-06 ***
## condition:trial    2.7      3   531.57    291   0.4880   0.69085    
## sex:trial          1.3      3   531.57    291   0.2441   0.86550    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## 
## Mauchly Tests for Sphericity
## 
##                 Test statistic    p-value
## trial                  0.78252 0.00027414
## condition:trial        0.78252 0.00027414
## sex:trial              0.78252 0.00027414
## 
## 
## Greenhouse-Geisser and Huynh-Feldt Corrections
##  for Departure from Sphericity
## 
##                  GG eps Pr(>F[GG])    
## trial           0.87585  2.387e-05 ***
## condition:trial 0.87585     0.6659    
## sex:trial       0.87585     0.8404    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
##                    HF eps   Pr(>F[HF])
## trial           0.9024575 1.884721e-05
## condition:trial 0.9024575 6.715529e-01
## sex:trial       0.9024575 8.462020e-01
## Anova Table (Type 3 tests)
## 
## Response: helpless_rating
##            Effect           df   MSE        F  pes p.value
## 1       condition        1, 97 12.02  9.37 **  .09    .003
## 2             sex        1, 97 12.02     1.79  .02     .18
## 3           trial 2.63, 254.87  2.09 9.19 ***  .09  <.0001
## 4 condition:trial 2.63, 254.87  2.09     0.49 .005     .67
## 5       sex:trial 2.63, 254.87  2.09     0.24 .003     .84
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '+' 0.1 ' ' 1
## 
## Sphericity correction method: GG
##  contrast  estimate    SE  df t.ratio p.value
##  X15 - X30    0.757 0.198 291  3.824  0.0008 
##  X15 - X45    0.644 0.198 291  3.251  0.0051 
##  X15 - X60    0.992 0.198 291  5.010  <.0001 
##  X30 - X45   -0.113 0.198 291 -0.573  0.5672 
##  X30 - X60    0.235 0.198 291  1.186  0.4733 
##  X45 - X60    0.348 0.198 291  1.759  0.2391 
## 
## Results are averaged over the levels of: condition, sex 
## P value adjustment: holm method for 6 tests
## Call:
## bwtrim(formula = helpless_rating ~ condition * factor(trial), 
##     id = ID, data = ratings)
## 
##                           value df1     df2 p.value
## condition               12.5040   1 68.7409  0.0007
## factor(trial)            5.4474   3 60.8077  0.0022
## condition:factor(trial)  1.2419   3 60.8077  0.3024

As expected, YC reported greater feelings of helplessness compared to EC. Overall helplessness ratings decreased across trials.

6 Changes in Affective State

6.1 Depression and Anxiety (STADI)

There were some outliers with respect to STADI scores but they did not represent extreme outliers, thus we kept them.

## 
## Univariate Type III Repeated-Measures ANOVA Assuming Sphericity
## 
##                Sum Sq num Df Error SS den Df   F value    Pr(>F)    
## (Intercept)    235896      1  11570.7     97 1977.5808 < 2.2e-16 ***
## condition         443      1  11570.7     97    3.7106  0.056996 .  
## sex                66      1  11570.7     97    0.5491  0.460471    
## time              154      1   1355.6     97   11.0002  0.001283 ** 
## condition:time      3      1   1355.6     97    0.1955  0.659392    
## sex:time            6      1   1355.6     97    0.4408  0.508312    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## Anova Table (Type 3 tests)
## 
## Response: STADI_S_Global
##           Effect    df    MSE        F  pes p.value
## 1      condition 1, 97 119.29   3.71 +  .04     .06
## 2            sex 1, 97 119.29     0.55 .006     .46
## 3           time 1, 97  13.97 11.00 **  .10    .001
## 4 condition:time 1, 97  13.97     0.20 .002     .66
## 5       sex:time 1, 97  13.97     0.44 .005     .51
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '+' 0.1 ' ' 1
## Call:
## bwtrim(formula = STADI_S_Global ~ condition * factor(time), id = ID, 
##     data = affStates)
## 
##                         value df1     df2 p.value
## condition              2.9723   1 60.9630  0.0898
## factor(time)           9.4166   1 69.5219  0.0031
## condition:factor(time) 0.1273   1 69.5219  0.7223

There was a trend effect of group with YC showing slightly higher scores than EC at pre and post. Although both groups reported an sig. increase in depressive symptoms and anxiety from pre to post stress induction, there was no interaction effect, i.e. no differential changes in STADI scores.

6.2 Positive and Negative Mood (PANAS)

6.2.1 Positive Mood

There were no outliers with respect to positive mood scores.

## 
## Univariate Type III Repeated-Measures ANOVA Assuming Sphericity
## 
##                Sum Sq num Df Error SS den Df   F value    Pr(>F)    
## (Intercept)    142384      1  10798.7     97 1278.9635 < 2.2e-16 ***
## condition          21      1  10798.7     97    0.1857   0.66749    
## sex               165      1  10798.7     97    1.4796   0.22679    
## time              460      1   1976.7     97   22.5583  7.05e-06 ***
## condition:time      8      1   1976.7     97    0.3892   0.53420    
## sex:time          137      1   1976.7     97    6.7410   0.01089 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## Anova Table (Type 3 tests)
## 
## Response: PANAS_pos
##           Effect    df    MSE         F  pes p.value
## 1      condition 1, 97 111.33      0.19 .002     .67
## 2            sex 1, 97 111.33      1.48  .02     .23
## 3           time 1, 97  20.38 22.56 ***  .19  <.0001
## 4 condition:time 1, 97  20.38      0.39 .004     .53
## 5       sex:time 1, 97  20.38    6.74 *  .06     .01
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '+' 0.1 ' ' 1

There were no group differences in positive mood but an overall decrease from pre to post stress induction. Men displayed a slightly smaller decrease compared to women.

6.2.2 Negative Mood

There were some outliers with respect to negative mood but since they did not affect results, we kept them.

## 
## Univariate Type III Repeated-Measures ANOVA Assuming Sphericity
## 
##                Sum Sq num Df Error SS den Df   F value    Pr(>F)    
## (Intercept)     36148      1   3338.9     97 1050.1721 < 2.2e-16 ***
## condition         268      1   3338.9     97    7.7901  0.006327 ** 
## sex                 0      1   3338.9     97    0.0078  0.929725    
## time               35      1    408.8     97    8.2540  0.004995 ** 
## condition:time      0      1    408.8     97    0.0646  0.799909    
## sex:time            2      1    408.8     97    0.3594  0.550244    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## Anova Table (Type 3 tests)
## 
## Response: PANAS_neg
##           Effect    df   MSE       F    pes p.value
## 1      condition 1, 97 34.42 7.79 **    .07    .006
## 2            sex 1, 97 34.42    0.01 <.0001     .93
## 3           time 1, 97  4.21 8.25 **    .08    .005
## 4 condition:time 1, 97  4.21    0.06  .0007     .80
## 5       sex:time 1, 97  4.21    0.36   .004     .55
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '+' 0.1 ' ' 1
## Call:
## bwtrim(formula = PANAS_neg ~ condition * factor(time), id = ID, 
##     data = affStates)
## 
##                         value df1     df2 p.value
## condition              6.7716   1 57.8746  0.0117
## factor(time)           6.9370   1 69.6631  0.0104
## condition:factor(time) 0.0000   1 69.6631  0.9950

There were sig. group differences in negative mood with slightly higher overall scores in YC compared to EC. We observed an overall decrease from pre to post stress induction but no interaction of group x time.

7 Escape Behaviour

7.1 Activity (moves per minute)

There were some outliers with respect to activity but few of them represented extreme deviations and it didn’t seem warranted to exclude them.

## 
## Univariate Type III Repeated-Measures ANOVA Assuming Sphericity
## 
##                               Sum Sq num Df Error SS den Df  F value    Pr(>F)
## (Intercept)                 51336095      1  8033840     97 619.8283 < 2.2e-16
## condition                      78797      1  8033840     97   0.9514  0.331791
## sex                           940303      1  8033840     97  11.3531  0.001082
## phase                        3102641      1  3410501     97  88.2440 2.733e-15
## condition:phase                38452      1  3410501     97   1.0936  0.298269
## sex:phase                      78431      1  3410501     97   2.2307  0.138539
## block                        1024142      1  1896256     97  52.3884 1.075e-10
## condition:block                48237      1  1896256     97   2.4675  0.119481
## sex:block                      28828      1  1896256     97   1.4747  0.227558
## trial                         627173      4  2008659    388  30.2868 < 2.2e-16
## condition:trial                11529      4  2008659    388   0.5567  0.694213
## sex:trial                      43262      4  2008659    388   2.0892  0.081543
## phase:block                     2743      1   610867     97   0.4355  0.510874
## condition:phase:block            556      1   610867     97   0.0882  0.767069
## sex:phase:block                   70      1   610867     97   0.0112  0.916052
## phase:trial                    21661      4  1587399    388   1.3236  0.260500
## condition:phase:trial          12205      4  1587399    388   0.7458  0.561270
## sex:phase:trial                21539      4  1587399    388   1.3162  0.263277
## block:trial                   258053      4  1960415    388  12.7683 8.984e-10
## condition:block:trial          31785      4  1960415    388   1.5727  0.180799
## sex:block:trial                15728      4  1960415    388   0.7782  0.539854
## phase:block:trial              41121      4  1373728    388   2.9036  0.021730
## condition:phase:block:trial    37479      4  1373728    388   2.6464  0.033203
## sex:phase:block:trial          59233      4  1373728    388   4.1825  0.002503
##                                
## (Intercept)                 ***
## condition                      
## sex                         ** 
## phase                       ***
## condition:phase                
## sex:phase                      
## block                       ***
## condition:block                
## sex:block                      
## trial                       ***
## condition:trial                
## sex:trial                   .  
## phase:block                    
## condition:phase:block          
## sex:phase:block                
## phase:trial                    
## condition:phase:trial          
## sex:phase:trial                
## block:trial                 ***
## condition:block:trial          
## sex:block:trial                
## phase:block:trial           *  
## condition:phase:block:trial *  
## sex:phase:block:trial       ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## 
## Mauchly Tests for Sphericity
## 
##                             Test statistic   p-value
## trial                              0.51861 0.000e+00
## condition:trial                    0.51861 0.000e+00
## sex:trial                          0.51861 0.000e+00
## phase:trial                        0.67748 2.480e-05
## condition:phase:trial              0.67748 2.480e-05
## sex:phase:trial                    0.67748 2.480e-05
## block:trial                        0.67189 1.791e-05
## condition:block:trial              0.67189 1.791e-05
## sex:block:trial                    0.67189 1.791e-05
## phase:block:trial                  0.73656 6.068e-04
## condition:phase:block:trial        0.73656 6.068e-04
## sex:phase:block:trial              0.73656 6.068e-04
## 
## 
## Greenhouse-Geisser and Huynh-Feldt Corrections
##  for Departure from Sphericity
## 
##                              GG eps Pr(>F[GG])    
## trial                       0.73144  < 2.2e-16 ***
## condition:trial             0.73144   0.639643    
## sex:trial                   0.73144   0.103447    
## phase:trial                 0.84760   0.264662    
## condition:phase:trial       0.84760   0.540669    
## sex:phase:trial             0.84760   0.267232    
## block:trial                 0.84766  1.308e-08 ***
## condition:block:trial       0.84766   0.190106    
## sex:block:trial             0.84766   0.520903    
## phase:block:trial           0.85153   0.028885 *  
## condition:phase:block:trial 0.85153   0.041956 *  
## sex:phase:block:trial       0.85153   0.004366 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
##                                HF eps   Pr(>F[HF])
## trial                       0.7566489 3.367593e-17
## condition:trial             0.7566489 6.455367e-01
## sex:trial                   0.7566489 1.011619e-01
## phase:trial                 0.8820095 2.637884e-01
## condition:phase:trial       0.8820095 5.456094e-01
## sex:phase:trial             0.8820095 2.664079e-01
## block:trial                 0.8820755 7.136785e-09
## condition:block:trial       0.8820755 1.879903e-01
## sex:block:trial             0.8820755 5.254546e-01
## phase:block:trial           0.8862748 2.701715e-02
## condition:phase:block:trial 0.8862748 3.971277e-02
## sex:phase:block:trial       0.8862748 3.831438e-03
## Anova Table (Type 3 tests)
## 
## Response: mpm
##                         Effect           df      MSE         F   pes p.value
## 1                    condition        1, 97 82823.09      0.95  .010     .33
## 2                          sex        1, 97 82823.09  11.35 **   .10    .001
## 3                        phase        1, 97 35159.81 88.24 ***   .48  <.0001
## 4              condition:phase        1, 97 35159.81      1.09   .01     .30
## 5                    sex:phase        1, 97 35159.81      2.23   .02     .14
## 6                        block        1, 97 19549.03 52.39 ***   .35  <.0001
## 7              condition:block        1, 97 19549.03      2.47   .02     .12
## 8                    sex:block        1, 97 19549.03      1.47   .01     .23
## 9                        trial 2.93, 283.80  7077.75 30.29 ***   .24  <.0001
## 10             condition:trial 2.93, 283.80  7077.75      0.56  .006     .64
## 11                   sex:trial 2.93, 283.80  7077.75      2.09   .02     .10
## 12                 phase:block        1, 97  6297.60      0.44  .004     .51
## 13       condition:phase:block        1, 97  6297.60      0.09 .0009     .77
## 14             sex:phase:block        1, 97  6297.60      0.01 .0001     .92
## 15                 phase:trial 3.39, 328.87  4826.86      1.32   .01     .26
## 16       condition:phase:trial 3.39, 328.87  4826.86      0.75  .008     .54
## 17             sex:phase:trial 3.39, 328.87  4826.86      1.32   .01     .27
## 18                 block:trial 3.39, 328.89  5960.67 12.77 ***   .12  <.0001
## 19       condition:block:trial 3.39, 328.89  5960.67      1.57   .02     .19
## 20             sex:block:trial 3.39, 328.89  5960.67      0.78  .008     .52
## 21           phase:block:trial 3.41, 330.39  4157.86    2.90 *   .03     .03
## 22 condition:phase:block:trial 3.41, 330.39  4157.86    2.65 *   .03     .04
## 23       sex:phase:block:trial 3.41, 330.39  4157.86   4.18 **   .04    .004
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '+' 0.1 ' ' 1
## 
## Sphericity correction method: GG

There was no main effect of group but a significant difference in activity between the free exploration phase and the stress phase as well as between blocks and across trials. Participants showed increased activity over time and blocks and generally lower activity in the stress phase. Complex interaction effects…

7.2 Escapes

There were no outliers with respect to escape rate.

## 
## Univariate Type III Repeated-Measures ANOVA Assuming Sphericity
## 
##                 Sum Sq num Df Error SS den Df  F value  Pr(>F)    
## (Intercept)     821.89      1   399.20     97 199.7056 < 2e-16 ***
## condition         0.54      1   399.20     97   0.1315 0.71768    
## sex              10.10      1   399.20     97   2.4548 0.12042    
## block            13.11      1   227.85     97   5.5809 0.02015 *  
## condition:block  11.51      1   227.85     97   4.9010 0.02918 *  
## sex:block         7.64      1   227.85     97   3.2506 0.07450 .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## Anova Table (Type 3 tests)
## 
## Response: sum_escapes_block
##            Effect    df  MSE      F  pes p.value
## 1       condition 1, 97 4.12   0.13 .001     .72
## 2             sex 1, 97 4.12   2.45  .02     .12
## 3           block 1, 97 2.35 5.58 *  .05     .02
## 4 condition:block 1, 97 2.35 4.90 *  .05     .03
## 5       sex:block 1, 97 2.35 3.25 +  .03     .07
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '+' 0.1 ' ' 1
##  contrast      estimate    SE  df t.ratio p.value
##  EC,X1 - YC,X1  -0.6021 0.371 181 -1.624  0.4382 
##  EC,X1 - EC,X2  -1.0254 0.276  97 -3.720  0.0020 
##  EC,X1 - YC,X2  -0.6378 0.371 181 -1.717  0.4382 
##  YC,X1 - EC,X2  -0.4233 0.371 181 -1.140  0.7679 
##  YC,X1 - YC,X2  -0.0358 0.353  97 -0.101  0.9196 
##  EC,X2 - YC,X2   0.3875 0.371 181  1.045  0.7679 
## 
## Results are averaged over the levels of: sex 
## P value adjustment: holm method for 6 tests
## Call:
## bwtrim(formula = sum_escapes_block ~ condition * factor(block), 
##     id = ID, data = escapesStress)
## 
##                          value df1     df2 p.value
## condition               0.1032   1 64.2822  0.7490
## factor(block)           3.9775   1 68.5782  0.0501
## condition:factor(block) 7.0282   1 68.5782  0.0100

EC managed to escape more often in block 2 compared to block 1, whereas YC did not improve (scores denote rather a slight decrease!). Overall participants escaped more often in block 2. Men improved more than women from block 1 to block 2.

7.3 Exploration

There were some outlier with respect to exploration but since they did not affect results, we kept them.

## 
## Univariate Type III Repeated-Measures ANOVA Assuming Sphericity
## 
##                               Sum Sq num Df Error SS den Df  F value    Pr(>F)
## (Intercept)                 58881195      1  9046665     97 631.3350 < 2.2e-16
## condition                     113890      1  9046665     97   1.2212   0.27187
## sex                          1053931      1  9046665     97  11.3004   0.00111
## phase                        3101927      1  3109569     97  96.7616 3.019e-16
## condition:phase                44758      1  3109569     97   1.3962   0.24025
## sex:phase                      92948      1  3109569     97   2.8994   0.09181
## block                        1122034      1  1955799     97  55.6485 3.703e-11
## condition:block                14083      1  1955799     97   0.6985   0.40536
## sex:block                      85588      1  1955799     97   4.2448   0.04205
## trial                        1079236      4  2230643    388  46.9308 < 2.2e-16
## condition:trial                 3514      4  2230643    388   0.1528   0.96169
## sex:trial                      73547      4  2230643    388   3.1982   0.01330
## phase:block                     7735      1   631430     97   1.1883   0.27838
## condition:phase:block           4207      1   631430     97   0.6463   0.42342
## sex:phase:block                 1481      1   631430     97   0.2276   0.63440
## phase:trial                    12282      4  1504282    388   0.7920   0.53089
## condition:phase:trial           4995      4  1504282    388   0.3221   0.86317
## sex:phase:trial                21189      4  1504282    388   1.3663   0.24497
## block:trial                   192152      4  2368431    388   7.8697 4.165e-06
## condition:block:trial          65567      4  2368431    388   2.6853   0.03115
## sex:block:trial                44953      4  2368431    388   1.8411   0.12019
## phase:block:trial              16311      4  1187061    388   1.3328   0.25708
## condition:phase:block:trial    33292      4  1187061    388   2.7204   0.02940
## sex:phase:block:trial          32894      4  1187061    388   2.6879   0.03102
##                                
## (Intercept)                 ***
## condition                      
## sex                         ** 
## phase                       ***
## condition:phase                
## sex:phase                   .  
## block                       ***
## condition:block                
## sex:block                   *  
## trial                       ***
## condition:trial                
## sex:trial                   *  
## phase:block                    
## condition:phase:block          
## sex:phase:block                
## phase:trial                    
## condition:phase:trial          
## sex:phase:trial                
## block:trial                 ***
## condition:block:trial       *  
## sex:block:trial                
## phase:block:trial              
## condition:phase:block:trial *  
## sex:phase:block:trial       *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## 
## Mauchly Tests for Sphericity
## 
##                             Test statistic  p-value
## trial                              0.48740 0.000000
## condition:trial                    0.48740 0.000000
## sex:trial                          0.48740 0.000000
## phase:trial                        0.74625 0.000983
## condition:phase:trial              0.74625 0.000983
## sex:phase:trial                    0.74625 0.000983
## block:trial                        0.58692 0.000000
## condition:block:trial              0.58692 0.000000
## sex:block:trial                    0.58692 0.000000
## phase:block:trial                  0.85865 0.104399
## condition:phase:block:trial        0.85865 0.104399
## sex:phase:block:trial              0.85865 0.104399
## 
## 
## Greenhouse-Geisser and Huynh-Feldt Corrections
##  for Departure from Sphericity
## 
##                              GG eps Pr(>F[GG])    
## trial                       0.71174  < 2.2e-16 ***
## condition:trial             0.71174    0.92027    
## sex:trial                   0.71174    0.02605 *  
## phase:trial                 0.88043    0.51682    
## condition:phase:trial       0.88043    0.84018    
## sex:phase:trial             0.88043    0.24917    
## block:trial                 0.79186  3.059e-05 ***
## condition:block:trial       0.79186    0.04373 *  
## sex:block:trial             0.79186    0.13632    
## phase:block:trial           0.92943    0.25920    
## condition:phase:block:trial 0.92943    0.03308 *  
## sex:phase:block:trial       0.92943    0.03479 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
##                                HF eps   Pr(>F[HF])
## trial                       0.7355075 2.443288e-24
## condition:trial             0.7355075 9.250713e-01
## sex:trial                   0.7355075 2.462910e-02
## phase:trial                 0.9176656 5.213944e-01
## condition:phase:trial       0.9176656 8.478121e-01
## sex:phase:trial             0.9176656 2.478935e-01
## block:trial                 0.8217060 2.296138e-05
## condition:block:trial       0.8217060 4.164536e-02
## sex:block:trial             0.8217060 1.338942e-01
## phase:block:trial           0.9710776 2.579624e-01
## condition:phase:block:trial 0.9710776 3.085603e-02
## sex:phase:block:trial       0.9710776 3.250938e-02
## Anova Table (Type 3 tests)
## 
## Response: exploration
##                         Effect           df      MSE         F  pes p.value
## 1                    condition        1, 97 93264.59      1.22  .01     .27
## 2                          sex        1, 97 93264.59  11.30 **  .10    .001
## 3                        phase        1, 97 32057.41 96.76 ***  .50  <.0001
## 4              condition:phase        1, 97 32057.41      1.40  .01     .24
## 5                    sex:phase        1, 97 32057.41    2.90 +  .03     .09
## 6                        block        1, 97 20162.88 55.65 ***  .36  <.0001
## 7              condition:block        1, 97 20162.88      0.70 .007     .41
## 8                    sex:block        1, 97 20162.88    4.24 *  .04     .04
## 9                        trial 2.85, 276.15  8077.53 46.93 ***  .33  <.0001
## 10             condition:trial 2.85, 276.15  8077.53      0.15 .002     .92
## 11                   sex:trial 2.85, 276.15  8077.53    3.20 *  .03     .03
## 12                 phase:block        1, 97  6509.58      1.19  .01     .28
## 13       condition:phase:block        1, 97  6509.58      0.65 .007     .42
## 14             sex:phase:block        1, 97  6509.58      0.23 .002     .63
## 15                 phase:trial 3.52, 341.61  4403.56      0.79 .008     .52
## 16       condition:phase:trial 3.52, 341.61  4403.56      0.32 .003     .84
## 17             sex:phase:trial 3.52, 341.61  4403.56      1.37  .01     .25
## 18                 block:trial 3.17, 307.24  7708.64  7.87 ***  .08  <.0001
## 19       condition:block:trial 3.17, 307.24  7708.64    2.69 *  .03     .04
## 20             sex:block:trial 3.17, 307.24  7708.64      1.84  .02     .14
## 21           phase:block:trial 3.72, 360.62  3291.73      1.33  .01     .26
## 22 condition:phase:block:trial 3.72, 360.62  3291.73    2.72 *  .03     .03
## 23       sex:phase:block:trial 3.72, 360.62  3291.73    2.69 *  .03     .03
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '+' 0.1 ' ' 1
## 
## Sphericity correction method: GG

There was no main effect of group but a significant difference in exploration between the free exploration phase and the stress phase as well as between blocks and across trials. Participants showed increased exploration over time and blocks and generally lower exploration in the stress phase. The interaction of condition x phase x trial indicated that YC explored much more during the stress phase than EC and this difference became more pronounced over trials.

7.4 Efficiency

There were some outliers with respect to efficiency but excluding them did not affect the results, so we kept them.

## 
## Univariate Type III Repeated-Measures ANOVA Assuming Sphericity
## 
##                  Sum Sq num Df Error SS den Df  F value    Pr(>F)    
## (Intercept)     1567728      1   408847     92 352.7745 < 2.2e-16 ***
## condition          7523      1   408847     92   1.6928  0.196479    
## sex                1769      1   408847     92   0.3980  0.529686    
## block              9880      1   311431     92   2.9188  0.090925 .  
## condition:block   36074      1   311431     92  10.6567  0.001541 ** 
## sex:block         14371      1   311431     92   4.2453  0.042183 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## Anova Table (Type 3 tests)
## 
## Response: overall_efficiency
##            Effect    df     MSE        F  pes p.value
## 1       condition 1, 92 4443.99     1.69  .02     .20
## 2             sex 1, 92 4443.99     0.40 .004     .53
## 3           block 1, 92 3385.11   2.92 +  .03     .09
## 4 condition:block 1, 92 3385.11 10.66 **  .10    .002
## 5       sex:block 1, 92 3385.11   4.25 *  .04     .04
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '+' 0.1 ' ' 1
##  contrast      estimate   SE  df t.ratio p.value
##  EC,X1 - YC,X1    15.39 13.2 181  1.166  0.6441 
##  EC,X1 - EC,X2    13.50 10.8  92  1.249  0.6441 
##  EC,X1 - YC,X2   -27.75 13.2 181 -2.104  0.1472 
##  YC,X1 - EC,X2    -1.89 13.2 181 -0.143  0.8863 
##  YC,X1 - YC,X2   -43.14 13.6  92 -3.178  0.0121 
##  EC,X2 - YC,X2   -41.25 13.2 181 -3.127  0.0121 
## 
## Results are averaged over the levels of: sex 
## P value adjustment: holm method for 6 tests
## Call:
## bwtrim(formula = overall_efficiency ~ condition * factor(block), 
##     id = ID, data = efficiencyStress)
## 
##                          value df1     df2 p.value
## factor(block)           1.9489   1 40.8194  0.1703
## condition               0.6105   1 33.9118  0.4400
## factor(block):condition 4.8779   1 33.9118  0.0341

Whereas EC and YC did not differ in efficiency in block 1 (although YC had slightly better scores), YC showed sig. less efficient behaviour in block 2 compared to EC. There was also an interaction of sex x block.

8 Plots for Paper

8.1 Figure 1

8.2 Figure 2